This research is funded by the National Science Foundation,
Div. of Physical Meteorology, and NASA, Division of Microgravity Science and
Applications.

Experiments in rotating cylindrical containers of fluid are carried to
generate data on the structure of thermally heated turbulent motions that are
strongly influenced by basic system rotation. Such rotationally
constrained convective flows occur in stars, planetary atmospheres and in the
Earth's oceans. Experimental results are compared with computational
simulations of rotating convection by our collaborators: Joe Werne,
Keith Julien and Nic
Brummell. The experiments extend the direct numerical simulation
results by going several orders of magnitude higher in Rayleigh number (a
measure of thermal forcing) and Taylor number (a measure of system rotation),
than can be attained with present computers.

Research Assistant Scott Kittelman with the rotating cell.

Sketch of the rotating flow. The heating generates cyclonic
plumes. These interact at moderate rotation levels to produce a mean
meridional overturning circulation that precesses in the anti-cyclonic sense
(opposite to the basic rotation Omega). This precessing cell is most
easily detected by comparing temperature time series at the side of the
container (at mid-depth), with measurements at the center point (as shown in the
above cartoon).

For example, in the precessing mean flow regime, the side probe shows a long
period oscillation associated with the successive arrivals of the hot and cold branches of
the mean meridional cell. The high frequency content of these time series
is due to convective plumes.

Measurements of the statistics of
temperature fluctuations at the center of the cell indicate that if the Rayleigh
number is large enough, there is a substantial range of basic rotation over
which there is Gaussian behavior associated with lateral mixing by
vortices. At lower thermal forcing exponential statistics are found at
all rotation rates.

At zero Taylor number [Ta = (2*Omega*H*H/viscosity)^2, where Omega is
basic rotation frequency and H is the depth of the cell ], Gaussian statistics
are found at large but not extreme values of the Rayleigh number Ra, which
measure the strength of the thermal forcing. At very large Ra and Ta = 0
the statistics are exponential. As Ta is raised the width of the Gaussian
region shrinks, so that at moderately large Ra, exponential statistics are
observed for all Ta. However, as Ra becomes large enough so that the
rotating turbulence is very vigorous, the Gaussian region returns. We have
quantified this by measuring the deviation from Gaussian behavior.

At PDF level 0.001 we fit the data and measure the distance of the curve from
Gaussian (0) to exponential (1.0) statistics. The following plot
summarizes the results.

The smallest cylinder with the the weakest imposed temperature difference dT
has the lowest Rayleigh number. The range of Guassian behavior (or
equivalently of sub-exponential statistics) is smaller than that for our large
cylindrical tank with dT = 10C (in which the Rayleigh number is of order 10^12).